A349273 Number of odd divisors of prime(n) - 1.
1, 1, 1, 2, 2, 2, 1, 3, 2, 2, 4, 3, 2, 4, 2, 2, 2, 4, 4, 4, 3, 4, 2, 2, 2, 3, 4, 2, 4, 2, 6, 4, 2, 4, 2, 6, 4, 5, 2, 2, 2, 6, 4, 2, 3, 6, 8, 4, 2, 4, 2, 4, 4, 4, 1, 2, 2, 8, 4, 4, 4, 2, 6, 4, 4, 2, 8, 4, 2, 4, 2, 2, 4, 4, 8, 2, 2, 6, 3, 4, 4, 8, 4, 4, 4, 4, 2, 4, 4, 8, 2, 2, 6, 6, 4
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Magma
[NumberOfDivisors(p-1)/Valuation(2*p-2, 2): p in PrimesUpTo(500)];
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Maple
nod:= n -> numtheory:-tau(n/2^padic:-ordp(n,2)): map(nod, [seq(ithprime(i)-1,i=1..100)]); # Robert Israel, Oct 11 2024
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Mathematica
a[n_] := DivisorSigma[0, (k = Prime[n] - 1)/2^IntegerExponent[k, 2]]; Array[a, 100] (* Amiram Eldar, Jun 03 2021 *) Count[Divisors[#-1],?OddQ]&/@Prime[Range[100]] (* _Harvey P. Dale, Jan 22 2024 *)
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PARI
a(n) = sumdiv(prime(n)-1, d, d%2); \\ Michel Marcus, Dec 18 2021
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Python
from sympy import divisors, prime def a(n): return sum(d%2 for d in divisors(prime(n)-1)) print([a(n) for n in range(1, 96)]) # Michael S. Branicky, Jul 04 2021
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